$A$ $B$ $C$ If: $ AC = 129$, $ BC = 9x + 4$, and $ AB = 8x + 6$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 6} + {9x + 4} = {129}$ Combine like terms: $ 17x + 10 = {129}$ Subtract $10$ from both sides: $ 17x = 119$ Divide both sides by $17$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 9({7}) + 4$ Simplify: $ {BC = 63 + 4}$ Simplify to find ${BC}$ : $ {BC = 67}$